Chapter 1 Geometry (Holt McDougal)

Acute Angle

An angle that measures greater than 0 and less than 90.

Adjacent Angles

Two angles in the same plane with a common vertex and a common side, but no common interior points.

Angle

A figure formed by two rays with a common endpoint.

Angle Bisector

A ray that divides an angle into two congruent angles.

Area

The number of nonoverlapping unit squares of a given size that will exactly cover the interior of a plane figure.

Base

The base b can be any side of a triangle. The best side to use for the base is the one opposite the vertex used when finding the height.

Between

Given 3 points A, B, and C,
B is between A and C if and only if
all 3 of the points lie on the same line.

Bisect

To divide into two congruent parts.

Circumference

The distance around the edge of a circle.
Circumference = (2)(?)(radius)

Collinear

Points that line on the same line.

Complementary Angles

Two angles whose measures have a sum of 90 degrees.

Congruent Angles

Angles that have the same measure.

Congruent Segments

Two segments that have the same length.

Construction

A mathematically precise figure that has been created using methods such as a compass and a straightedge, geometry software, or paper folding.

Coordinate

A number that identifies the location of a point on a number line. On the coordinate plane, the x and y-coordinates are used. In 3D space use 3 coordinates (x,y,z).

Coordinate Plane

A plane that is divided into four regions (quadrants) by a horizontal line called the x-axis
and a vertical line called the y-axis.

Coplanar

Points that line in the same plane.

Degree

A unit of angle measure; one degree is 1/360 of a circle.

Diameter

A segment that has endpoints on the circle and that passes through the center of the circle; also the length of that segment. Diameter = (2)(radius)

Distance

(On the Number Line) The absolute value of the difference of the coordinates of the points.
(Coord. Plane) D = sqrt[ (x2 - x1)^2 + (y2 - y1)^2 ]

Endpoint

A point at the end of a segment,
or the starting point of a ray.

Exterior of an Angle

The set of all points outside the an angle.

Height

The length of an altitude of a figure.

Hypotenuse

The side opposite the right angle angle in a right triangle.

Image

A shape that results from a transformation of a figure known as the preimage

Interior of an Angle

The set of all points between the sides of an angle.

Legs of a Triangle

The two sides of the right triangle that form the right triangle.

Length

The distance between two endpoints
of a segment.

Line

An undefined term in geometry, a line is a straight path that has no thickness and extends forever.

Linear Pair

A pair of adjacent angles whose noncommon sides are opposites rays. The sum of the angles in a linear pair is 180 degrees.

Measure of an Angle

Angles are measured in degrees.

Obtuse Angle

An angle that measures greater than 90 degrees and less than 180 degrees.

Opposite Rays

Two rays that have a common endpoint and form a line.

Perimeter

The sum of the side lengths of a closed plane figure.

Plane

An undefined term in geometry, it is a flat surface that has no thickness and extends forever.

Point

An undefined term in geometry, it names a location and has no size.

Postulate

A statement that is accepted as true without proof.

Preimage

The original figure in a transformation.

Radius of a Circle

A segment whose endpoints are the center of a circle and a point on the circle; the distance from the center of a circle to any point on the circle.

Ray

A part of a line that starts at an endpoint and extends forever in one direction.

Reflection

A transformation across a line of reflection,
the l.o.r. is the perpendicular bisector of each segment joining each point and its image.

Right Angle

An angle whose measure is 90 degrees.

Rotation

A transformation about the point P, known as the center of rotation, such that each point and its image are the same distance from P.

Segment of a Line

A part of a line consisting of two endpoints and all points between them.

Segment Bisector

A line, ray, or segment that divides a segment into two congruent segments.

Straight Angle

A 180 degree angle.

Supplementary Angles

Two angles whose measures have a sum of 180 degrees.

Transformation

A change in the position, size, or shape
of a figure or a graph.

Translation

A transformation that shifts or slides every point of a figure or graph the same distance in the same direction.

Undefined Terms

The undefined terms in geometry are point, line, and plane.

Vertex of an Angle

The common endpoint of the sides of the angle.

Vertical Angles

The nonadjacent angles formed by two intersecting lines.

Pi

The ratio of the circumference of a circle to its diameter, denoted by the Greek letter ? (pi). The value of pi is irrational, often shortened to 3.14 or 22/7 .

Midpoint

The point that joins the segment into two congruent segments. If A(x1,y1) and B(x2,y2), then midpoint M[ (x1 + x2) / 2 , (y1 + y2) / 2 ] ) .

Postulate 1-1-1

Through any two points there is exactly one line.

Postulate 1-1-2

Through any three noncollinear points there is exactly one plane containing them.

Postulate 1-1-3

If two points lie in a plane, then the line containing those points lies in the plane.

Postulate 1-1-4

If two lines intersect, then they intersect in exactly one point.

Postulate 1-1-5

If two planes intersect, then they intersect in exactly one line.

Ruler Postulate

The points on a line can be put into a one-to-one correspondence with the real numbers.

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Protractor Postulate

Given AB and a point O on AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180 degrees.

Angle Addition Postulate

If S is in the interior of ?PQR,
then m?PQS + m?SQR = m?PQR

Pythagorean Theorem

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a^2 + b^2 = c^2